Equational unification of two terms consists of finding a substitution that, when applied to both terms, makes them equal modulo some equational properties. A narrowing-based equational unification algorithm relying on the concept of the variants of a term is available in the most recent version of Maude, version 3.0, which provides quite sophisticated unification features. A variant of a term t is a pair consisting of a substitution sigma and the canonical form of tsigma. Variant-based unification is decidable when the equational theory satisfies the finite variant property. However, this unification procedure does not take into account constructor symbols and, thus, may compute many more unifiers than the necessary or may not be able to stop immediately. In this paper, we integrate the notion of constructor symbol into the variant-based unification algorithm. Our experiments on positive and negative unification problems show an impressive speedup.

中文翻译：

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构造函数符号下基于变体的方程统一

两项的等式统一包括找到一个替代，当应用于这两项时，使它们以某些等式属性为模相等。最新版本的 Maude 3.0 版提供了一种依赖于术语变体概念的基于缩小的等式统一算法，该算法提供了非常复杂的统一功能。术语 t 的一个变体是由替换 sigma 和 tsigma 的规范形式组成的对。当方程理论满足有限变体性质时，基于变体的统一是可判定的。然而，这个统一过程没有考虑构造函数符号，因此，可能计算出比必要的多得多的统一词，或者可能无法立即停止。在本文中，我们将构造函数符号的概念整合到基于变体的统一算法中。我们在正面和负面统一问题上的实验显示出令人印象深刻的加速。